If we don't know that the true equation is x(t+1) = f(x(t),u(t)) but have to infer it from data, then observing that such an equation seems to hold true for some particular u and x does not mean that u causes changes to x.

It may simply be a predictor of x, as in the 'barometer readings may precede and imply a storm but not cause one' example given by others above.